Question

(3-√7) (3-√7)
is rational, irrational or
Negative integers

​

Answer 1

Step-by-step explanation:

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Answer 2

Given,

$\tt(3 - \sqrt{7} )(3 - \sqrt{7} )$

We Have,

• To determine whether the above mentioned expression is rational, or irrational, or negative integers.

So,

• Simplifying the expression,

Here,

• Expression is in form of (a - b)(a - b) i.e. (a - b)², then, formula used is

$\boxed{ \sf\bull \: \pink{ {(a - b)}^{2}} = \green{ {a}^{2} + {b}^{2} - 2ab}}$

Now,

$\bf \huge {(3 - \sqrt{7}) }^{2} \\ \bf \large \to {(3)}^{2} + {( \sqrt{7} )}^{2} - 2(3)( \sqrt{7} ) \\ \bf \large \to 9 + 7 - 6 \sqrt{7} \\ \bf \large \to \orange{16 - 6 \sqrt{7} }$

Since,

• Obtained expression has √7 which is irrational, thus, whole obtained expression is irrational number.

$\because \: \text{Operation like addition or subtraction } \\ \: \: \: \: \: \text{ of rational }{\&} \text{ irrational number} \\ \: \: \: \: \: \text {always results as irrational value.}$

Hence,

• (3-√7) (3-√7) is irrational number